Proportiones Perfectus Law and the Physics of the Golden Section
Journal Title: Asian Research Journal of Mathematics - Year 2017, Vol 7, Issue 1
Abstract
The proportiones perfectus law is introduced. Let σ_x^y=(x+√(x^2+4y))/2 . By definition, in the spectrum 1≤y≤x, x≥1, σ_x^y is a proportione perfectus. With σ_x^y so defined, for an arbitrary positive integer h_1 it is shown that there exists an integer sequence H_n satisfying the quasi-geometric relation h_(n+1)=round(σ_x^y h_n ),n≥1 such that the arithmetic relation h_(n+2)=〖xh〗_(n+1)+〖yh〗_n holds. The golden mean, designated σ_1^1 or φ, becomes the most basic and fundamental of proportiones perfectus. New concepts to the study of the golden section are presented: chirality, number genetics and law of polarity, special numerical harmony, and chemical geometry. A geometrical basis for the fine-structure constant in the golden section is established. Our stating of over forty theorems in this reading serves no other purpose than that of expanding the theory of the golden section while equipping the interested reader with instruments for further research and development of this science of number.
Authors and Affiliations
Lovemore Mamombe
Keywords
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- EP ID EP338327
- DOI 10.9734/ARJOM/2017/36860
- Views 157
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